3edt
3EDT, if the attempt is made to use it as an actual scale, would divide the tritave into three equal parts, each of size 633.9850 cents, which is to say 3^(1/3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out 9/8 as well as 2edo.
Theory
75/52 is a good rational representation of the cube root of 3.
Relationship to octave temperaments
3EDT is closely related to any rank-2 octavated temperament which takes 3 generators to reach the 3rd harmonic, of which there's a notable amount of.